Hey PT! I just started up an extra 1g tank I had laying around and decided to make a shrimp tank. As of right now, It holds 100% natural spring water from a natural spring close by. I used this water because I've read that shrimp do fine in it, opposed to my shrimp-killing well water filled with copper. I've tried shrimp before, but all died due to the copper in my house water. I have to cycle the tank, but I don't know how to do it- With my betta in the well established 5g, or a fishless, which I don't know what to do.
As of now, here are the specs:
Tank:
Temp: 72° F
7w CF Bulb
Mini-HOB Filter
Plain Black Gravel
Rock
Little Plantlet of Watersprite
Parameters:
pH: 7.6
Ammonia: 0ppm
NitrIte: 0ppm
NitrAte: 0ppm
Here is a picture of the tank:

Should I cycle the tank with my Betta, or do a fishless cycle(please explain how to do)?
Thanks,
Smalltank